Dashen-Frautschi Fiasco

On April 29, at the 1965 spring meeting of the American Physical
Society in Washington, Freeman J. Dyson of the Institute of Advanced
Study (Princeton) presented an invited talk entitled
"Old and New Fashions in Field Theory," and the content of his talk
was published in the June issue of the Physic Today, on page 21-24.
This paper contains the following paragraph.

The first of these two achievements is the explanation
of the mass difference between neutron
and proton by Roger Dashen, working at the time as a graduate
student under the supervision of Steve Frautschi.
The neutron-proton mass difference has for thirty years been believed
to be electromagnetic in origin, and it offers a splendid
experimental test of any theory which tries to cover the borderline
between electromagnetic and strong interactions. However,
no convincing theory of the mass-difference had appeared before
1964. In this connection I exclude as unconvincing all theories,
like the early theory of Feynman and Speisman, which use one
arbitrary cut-off parameter to fit one experimental number.
Dashen for the first time made an honest calculation without arbitrary
parameters and got the right answer. His method is a
beautiful marriage between old-fashioned electrodynamics and modern
bootstrap techniques. He writes down the equations expressing
the fact that the neutron can be considered to be a bound state of a
proton with a negative pi meson, and the proton a bound state of
a neutron with a positive pi meson, according to the bootstrap method.
Then into these equations he puts electromagnetic perturbations, the
interaction of a photon with both nucleon and pi meson, according to
the Feynman rules. The calculation of the resulting mass difference is
neither long nor hard to understand, and in my opinion, it will become
a classic in the history of physics.

Dyson was talking about the paper by R. F. Dashen and S. C. Frautschi
published in Phys. Rev. 135, B1190 and B1196 (1964). They use
the S-matrix formalism for bound states.

Later in the same year, Steve Adler and Roger Dashen became full
professors at the Institute for Advanced Study. Naturally, they were
admired by their colleagues, and many young physicists studied
Dashen's paper on the neutron-proton mass difference. I was one of
those who studied the paper carefully during the summer of 1965. I then
published a paper in the Physical Review [142, 1150 (1966)].

In their paper, Dashen and Frautschi use the S-matrix method to calculate
a perturbed energy level. Of course, they use approximations because
they are dealing with strong interactions. If we translate what they
did into the language of the Schrödinger picture, they are using the
following approximation for

(φ, δV φ),

There are however "good" and "bad" approximations.
I showed in my paper that Dashen and Frautschi use the formula

(φ good , δV φbad) .

I then pointed out their infrared divergence comes from this bad
approximation.

How could those two distinguished physicists make this kind of
mistake? If you solve the Schrödinger equation for negative
energy states, there are two solutions: "good" and "bad." We then
impose a localization condition to eliminate bad wave functions.
This results in a discrete spectrum of bound-state energy levels.
Thus a slight departure from a given energy level will result in
a bad wave function.
Click here for a recent article on this subject.

Dashen and Frautschi use the S-matrix formalism where the bound-states
appear as poles in the complex energy plane. A slight mislocation
will lead to the inclusion of the bad wave function. This is
precisely the course of the so-called "Dashen-Frautschi Fiasco."

I am indeed fortunate to have an excellent education in physics. I took
my first-year quantum mechanics when I was a senior (1957-58) at
Carnegie Tech (now called Carnegie Mellon University). Michel Baranger
was the professor, taught me why bound-state energy levels are discrete.
I still remember those good and bad wave functions he drew on the blackboard.

In 1997, I attended his 70th birthday celebration held at MIT. My
wife and I posed with him in this photo. We were very happy!

Toward a New Research Program

Feynman was on my side!

After publication of my paper, many voiced objections based on the
belief that Princeton could not have made this kind of mistake or
misjudgment. There were also many who knew Dashen's calculation was
wrong, but they were not sympathetic to me. Their assumption was that
I would disappear from the physics world. One prominent Princeton
professor told me wave functions have nothing to do with physics and
everything should come the S-matrix and the current algebra.

I am standing in front of Feynman's portrait at the entrance of
Fermi Lab's Feynman Computing Center (June 2003).

Since then, I became devoted to wave functions. In 1970, I was very
fortunate to find a very important person who shared the same ideology as
mine. His name was
Richard P. Feynman. People these days ask me what
connection I have with Feynman. This was
the very beginning of my Feynman connection. Yet, it takes time to
transform ideology to concrete results in physics. For this, I lived
in isolation for fifteen or twenty years (depending on how to count).
It was like living in prison. The person who pulled me out of prison
was
Eugene Paul Wigner,
and I am forever grateful to him.

As for the wave functions, I was particularly interested in their
localization property, as you can see from the "good" and "bad" wave
functions. The burning issue was and still is whether the hydrogen
wave function localized in one Lorentz frame appears to be localized to
observers in other Lorentz frames. This is a well-defined problem,
and I enjoyed working on this problem in the past. I enjoy giving
invited talks on this subject under current titles, such as
symmetries of extended particles, covariance of Feynman's parton
picture, Feynman's rest of the universe, squeezed states, Feynman's
decoherence, Wigner's little groups, and other trademarks of current
interest.